Una is setting up a spotlight on a screen that is 12 m high and sits on a stage 1 m high.The spotlight is mounted on a stand so is 1 m off the ground, but it is stuck at an angle of 420How far back from the stage must she be in order to cover the whole screen?Round to the nearest 2 decimal places. (Put the numbers only in the box, do not enter any units.)

Alice wants to take a picture of a historical building that is wide but not tall. From available references, she is able to find out that the building is 33 metres wide. She plans to take the picture standing directly in front of it, at a point perpendicular to the midpoint of the building. She is using a moderately wide-angle lens which provides an angle of coverage of 64◦. Alice sketches the situation as in Figure 7, where all lengths are measured in metres. The point A represents Alice’s position. Points B and C are at each end of the building. Point D is the midpoint of the building. The length of AB is equal to the length of AC. The angle BAD is 32◦. How far from the midpoint D should Alice stand in order to be able to take a picture of the whole building? (You can assume that the height of the building is not an issue)

From her eye, which stands 1.68 meters above the ground, Hannah measures the angle of elevation to the top of a prominent skyscraper to be 31degrees ∘ . If she is standing at a horizontal distance of 194 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

Jacqueline is flying a plane and is descending at a 14°14° angle towards a runway. If she can see a mountain behind her at a 55°55° angle that is 400400 yards away from the runway, how much further does she have to fly until she lands? Round to the nearest tenth.

Amy is up in the lighthouse tower looking out at the ship. She knows the lighthouse (BC) is 12.5 m tall.She measures the angle of depression to be 130How far (AC) out to sea is the ship from the base of the tower?Round to the nearest 2 decimal places. (Put the numbers only in the box, do not enter any units.)

An observer 1.6 m tall is 20root3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is: 21.6 m 23.2 m 24.72 m None of these